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The Kalman filter is an algorithm for estimating the mean vector and variance-covariance matrix of the unknown state in a state space model.

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Extended Kalman Filter Non-Linear Regression Implementation R, Correct?

In your model, beta is fixed, so you should set processNoise <- diag(c(0, 0)). By specifying non-zero variances for the state, you'd assume that the state (beta) is stochastic. As your initial guess …
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how to make Kalman filter results equivalent to linear regression?

Yes, this is possible by setting the process noise to zero, assuming your coefficients (which are in the state) are deterministic. The filtered estimate of the state at the final observation is then e …
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